=1608.= The _simple modes_ of _number_ are of all other the most distinct; every the least variation, which is an unit, making each combination as clearly different from that which approacheth nearest to it, as the most remote; two being as distinct from one, as two hundred; and the idea of two as distinct from the idea of three, as the magnitude of the whole earth is from that of a mite.--LOCKE, JOHN. _An Essay concerning Human Understanding, Bk. 2, chap. 16, sect. 3._ =1609.= The number of a class is the class of all classes similar to the given class.--RUSSELL, BERTRAND. _Principles of Mathematics (Cambridge, 1903), p. 115._ =1610.= Number is that property of a group of distinct things which remains unchanged during any change to which the group may be subjected which does not destroy the distinctness of the individual things.--FINE, H. B. _Number-system of Algebra (Boston and New York, 1890), p. 3._ =1611.= The science of arithmetic may be called the science of exact limitation of matter and things in space, force, and time. --PARKER, F. W. _Talks on Pedagogics (New York, 1894), p. 64._ =1612.= Arithmetic is the science of the Evaluation of Functions, Algebra is the science of the Transformation of Functions. --HOWISON, G. H. _Journal of Speculative Philosophy, Vol. 5, p. 175._ =1613.= That _arithmetic_ rests on pure intuition of _time_ is not so obvious as that geometry is based on pure intuition of space, but it may be readily proved as follows. All counting consists in the repeated positing of unity; only in order to know how often it has been posited, we mark it each time with a different word: these are the numerals. Now repetition is possible only through succession: but succession rests on the immediate intuition of _time_, it is intelligible only by means of this latter concept: hence counting is possible only by means of time.--This dependence of counting on _time_ is evidenced by the fact that in all languages multiplication is expressed by “times” [mal], that is, by a concept of time; sexies, ἑξακις, six fois, six times. --SCHOPENHAUER, A. _Die Welt als Vorstellung und Wille; Werke (Frauenstaedt) (Leipzig, 1877), Bd. 3, p. 39._ =1614.= The miraculous powers of modern calculation are due to three inventions: the Arabic Notation, Decimal Fractions and Logarithms.--CAJORI, F. _History of Mathematics (New York, 1897), p. 161._